Functional Analysis

If N' is a Banach space then B(N, N') is a

• normed linear space

• not a Banach space

• Banach space

• Linear space

N is said to be ............ to N' if there exists an isometric isomorphism of N onto N'.

• homomorphism

• isometrically homomorphism

• isomorphism

• isometrically isomorphism

A Banach space is a .................. space.

• complete

• quadratic

• linear

• compact

The ........... theorem enables us to give a satisfactory description of the projections on a Banach space.

• Hahn Banach

• Open Mapping

• closed mapping

• Boundedness

• linear

• vector

• scalar

• norm

The norm of a number x is defined by .....................

• standard norm

• norm

• uniform norm

• unit norm

• bounded

• continuous

• closed

• complete

The elements of N* are called ............................

• continuous linear functionals

• elements of N

• vector values

• scalar values

Which of the following is an example of a nls?

• W

• Z

• N

• C